Answer:
x = 10
Step-by-step explanation:
y = - 8 is a horizontal line parallel to the x- axis
A line perpendicular to it will therefore be a vertical line parallel to the y- axis with equation
x = c ( c is the value of the x- coordinates the line passes through )
the line passes through (10, - 20 ) with x- coordinate 10 , then
x = 10 ← equation of perpendicular line
WILL GIVE BRAINIEST!!!!!
The x-coordinates of the points of intersection of the given function graphs are;
1) x = 0 and x = 2
2) x = -1
3) x = 0
What is the point of intersection of the graph?The point of intersection of a graph is defined as the point or coordinates where two lines or curves meet each other.
1) In the first graph, we are given the functions as;
f(x) = -³/₄x² + 3x + 1
g(x) = 2ˣ
Thus;
From the graph, f(x) = g(x) is at (2,4 and (0, 1)
2) In the first graph, we are given the functions as;
f(x) = x² + 4x + 2
g(x) = (¹/₂)ˣ + 1
Thus;
From the graph, f(x) = g(x) is at (-1. 3)
C) In the third graph, we are given the functions as;
f(x) = -⁷/₃x - 3
g(x) = 2ˣ - 4
Thus;
From the graph, f(x) = g(x) is at (0, -3)
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Make a table of the values for the function Y=3/5x-1
Answer:
plug the the x values in the chart into the formula one at a time and plug it into a calculator to get your y values.
example: y= -3/5(10)-3 —-> -9 y value
Step-by-step explanation:
If the following fractions were converted to decimals, which one would result in a repeating decimal?
A. 3⁄7
B. 1⁄9
C. 3⁄4
D. 5⁄11
3/7 and 5/11 are fraction when converted in decimals resulted in repeating decimals.
Repeating decimals also known as recurring decimals means after decimals , a particular digit or sequence of digits keep repeating itself indefinitely . They are non terminating numbers means which don't have a end. Bars are used over that repeating digits .
Dividing the fractions :
A . 3/7 = 0.42857
It has different values after decimals
B. 1/9 = 0.111111
it has single value 1 which is repeating itself
C . 3/4 = 0.75
two different values after decimals
D. 5/11 = 0.4545454
after decimals 45 a sequence of number is repeating itself
3/7 and 5/11 are fraction which resulted into repeating decimals.
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-1.25(z+8)=-6
Please help; find z
Answer:
z = -3.2
Step-by-step explanation:
-1.25(z + 8) = -6
-1.25z - 10 = -6
+10 +10
-----------------------
-1.25z = 4
÷(-1.25) ÷(-1.25)
--------------------------
z = -3.2
I hope this helps!
2. The following data set is given:5041414546364436513736494345454136Construct a dot plot:
As given by the question
There are given that the numbers;
[tex]50,\text{ 41, 41, 45, 46, 36, 44, 36, 51, 37, 36, 49, 43, 45, 45, 41, 36.}[/tex]Now,
First make a table of numbers and their frequency.
So,
[tex]\begin{gathered} \text{Number}\rightarrow\text{frequency} \\ \text{ }36\rightarrow4 \\ \text{ 37}\rightarrow1 \\ \text{ }44\rightarrow1 \\ \text{ 45}\rightarrow3 \\ \text{ 46}\rightarrow1 \\ \text{ 49}\rightarrow1 \\ \text{ 50}\rightarrow1 \\ \text{ 51}\rightarrow1 \\ \text{ 41}\rightarrow3 \\ \text{ 43}\rightarrow1 \end{gathered}[/tex]Now,
From the dot plot of the given numbers and their frequency.
So,
The dot plot of the given number is shown below:
If the simple interest on $6,000 for 5 years is $2,400 then what is the interest rate?
The interest rate will be 8%.
What is Simple interest?
A quick and easy method of calculating the interest charge on a loan is called a Simple interest.
Given that;
Principal amount = $6,000
Time = 5 years
Simple interest = $2,400
Now,
We know that;
⇒ Simple interest = PRT
Where, P is principal amount, R is interest rate and T is time.
Substitute all the values, we get;
⇒ Simple interest = PRT/100
⇒ 2400 = 6,000 x R x 5/100
⇒ 2400/30,000 = R/100
⇒ R = 0.08 x 100
⇒ R = 8%
Thus, The interest rate will be 8%.
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Round 31.212 to the nearest hundredth.
☐
Answer:
31.21
Step-by-step explanation:
Write an equation of the line in point-slope form that passes through the given points. (-2,8) and (7,-4)
The equation of the line is y-8 = [tex]\frac{-4}{3}[/tex] ( x+2) .
What is equation of the line ?
A line's coordinate plane equation can be expressed in two point form. Depending on the information at hand, a line's equation can be discovered using a variety of techniques. One approach is the two-point form. When two points that are on the line are known, this is used to find the equation of the line. The slope intercept form, intercept form, point slope form, and other crucial forms for representing the line equation.
Here the given two points are ,
[tex](x_1,y_1)=(-2,8)\\(x_2,y_2)=(7,-4)[/tex]
Now using slope formula,
slope m= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
=> slope m = [tex]\frac{-4-8}{7+2}[/tex]
=> slope m = [tex]\frac{-12}{9}= \frac{-4}{3}[/tex]
Now using equation formula,
=> [tex]y-y_1 = m(x-x_1)\\[/tex]
=> y-8 = [tex]\frac{-4}{3}[/tex] ( x+2)
Hence the point slope form of the equation is y-8 = [tex]\frac{-4}{3}[/tex] ( x+2) .
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Find the derivative of y with respect to z.y = ln (sinh 9z)
The given function is:
[tex]y=\ln (\sinh 9z)[/tex]Differentiate w. r. t. z to get:
[tex]\begin{gathered} \frac{dy}{dz}=\frac{d}{dz}(\ln \sinh 9z) \\ =\frac{1}{\sinh9z}\frac{d}{dz}(\sinh 9z) \\ =\frac{1}{\sinh9z}\cosh 9z(\frac{d}{dz}9z) \\ =\frac{9\cosh 9z}{\sinh 9z} \\ =9\cot h9z \end{gathered}[/tex]Hence the derivative is 9cot9z.
1. Evaluate the expression using the order of operations. Show your work.
(due right now) Will mark brainliest + 20 points
Answer:
0.5
Step-by-step explanation:
-1 + 3[(10-12)³÷(-16)]
Step 1: (10 - 12)³ — Bracket
(-2)³ = -8
Step 2: -8 ÷ (-16) — Division
-8/-16
= 1/2
Step 3: 3(1/2) — Multiplication
= 3/2
Step 4: 1 + 3/2 — Addition
= 0.5
You can also type it straight into the calculator to confirm.
What is the common difference for the arithmetic sequence?
3.2, 5, 6.8, 8.6, 10.4
help me please!
Answer:
the difference is 1.8
Step-by-step explanation:
5-3.2=1.8
6.8-5=1.8
8.6-6.8=1.8
ect
60 feet per second = how many kilometers per hour?
For solving this problem we have to know the transformations between feeds and kilometers and seconds to hours:
[tex]\begin{gathered} 1\operatorname{km}=3280.84ft \\ 1h=3600\text{ seg} \end{gathered}[/tex]Now we can make the transformation:
[tex]60\frac{ft}{seg}=60\frac{1}{3280.84}\frac{3600}{1}=65.8\frac{\operatorname{km}}{h}[/tex]11 The table below shows pairs of values that satisfy a linear function.2 -53 64 175 286 397 50What is the y-intercept of the graph of this function?
10)
we get the points from the table are (2,12) and (8,0).
Consider the line equation.
[tex]y=mx+b[/tex]where b is the y=intercept.
Substitute x=2 and y=12, we get
[tex]12=m(2)+b[/tex][tex]12=2m+b[/tex][tex]12-b=2m[/tex][tex]\frac{12-b}{2}=m[/tex]Substitute x=8 and y=0 in the line equation, we get
[tex]0=8m+b[/tex]Substitute m value in this equation to find the value of b.
[tex]0=8(\frac{12-b}{2})+b[/tex][tex]0=4(12-b)+b[/tex][tex]0=4\times12-4b+b[/tex][tex]0=48-3b[/tex][tex]3b=48[/tex]Dividing both sides by 3, we get
[tex]b=\frac{48}{3}=16[/tex]Hence the y-intercept is 16.
11)
we get the points from the table are (2,-5) and (4,17).
Consider the liner function.
[tex]y=mx+b[/tex]where b is the y-intercept.
Substitute x=2 and y=-5, we get
[tex]-5=2m+b[/tex][tex]-5-b=2m[/tex][tex]\frac{-5-b}{2}=m[/tex][tex]m=\frac{-5-b}{2}[/tex]Substitute x=4 and y=17 in the equation, we get
[tex]17=4m+b[/tex]Substitute the value of m in this equation to find the value of b.
[tex]17=4(\frac{-5-b}{2})+b[/tex][tex]17=2(-5-b)+b[/tex][tex]17=-10-2b+b[/tex][tex]17+10=-b[/tex][tex]b=-27[/tex]Hence the y-intercept is -27.
Which equivalent equation is the result of applying the distributive property in thegiven equation?10y + 14 = 2(y-9)
Answer
[tex]10y+14=2y-18[/tex]Explanation
The distributive property tells us that:
[tex]a(x+y)=ax+ay[/tex]Thus, we can apply this property to our given equation in the right side:
[tex]10y+14=2(y-9)[/tex][tex]10y+14=(2\cdot y-2\cdot9)[/tex][tex]10y+14=2y-18[/tex]A yearbook has 32 pages, and each page has 8 pictures on it. Estimate how manypictures are in the yearbook.
To find how many picture are in the yearbook, multiply the number of pages of the yearbook by the number of pictures on one page. This is 32 times 8:
[tex]32\cdot8=256[/tex]There are 256 picture in the yearbook.
The equation of a circle centred at the origin with a radius of 3 units is defined by X^2 + Y^2=9. Determine the equations of the line passing through the point (0,5) that intersects the circle at exactly one point
The equations of the lines that pass through the point (0,5) and intersect the circle at exactly one point are y = 4/3x + 5 and y = -4/3x + 5.
The equation of a circle centred at the origin with a radius of 3 units is defined by x² + y² = 3². The coordinates of the point are (0, 5). Let the equation of the tangent be y = mx + c.
y = mx + c
5 = m(0) + c
c = 5
The equation of the tangent is of the form mx -y + 5 = 0. The distance of the centre of the circle from the tangent must be equal to the radius of the circle.
d = |ax + by + c|/√(a² + b²)
3 = |m(0) + (-1)(0) + 5|/√[m² + (-1)²]
√[m² + (-1)²] = 5/3
m² + 1 = 25/9
m² = 16/9
m = ±4/3
The equations of the tangents are y = 4/3x + 5 and y = -4/3x + 5.
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What is the approximate length of the track in miles
Explanation
Opposite sides are 5 miles each and for each semicircle we have:
[tex]\frac{2\pi *\frac{1}{2}}{2}=\frac{\pi}{2}\text{ miles}[/tex]Then the lenght of the track is:
[tex]5+5+\frac{\pi}{2}+\frac{\pi}{2}=10+\pi[/tex]Approximately 13.1416 miles
An irregular figure is shown on the coordinate plane below. Part A: Find the area of the irregular figure above. Answer:__________________________ square units
In the present question, we will calculate the area of each of the three regular figures that are parts of the irregular figure. They are:
A: a rectangle 4x3
B: a rectangle 9x3
C: a rectangle 3x5
The area of each rectangle is just the multiplication of the two sides, and the area of the irregular figure is the sum of them. From this, we calculate:
[tex]\begin{gathered} A_A=4\times3=12\text{ square units} \\ A_B=9\times3=27\text{ square units} \\ A_C=3\times5=15\text{ square units} \\ \\ A_{\text{Total}}=A_A+A_B+A_C \\ A_{\text{Total}}=12+27+15=54\text{ square units} \end{gathered}[/tex]From the solution presented above, we are able to conclude that the area of the irregular figure is 54 square units.5.5/x=1.375/11
find x
Answer:x=44
Step-by-step explanation:
draw the lewis structure for nh3. what are the approximate bond angles, in degrees, around the n atom?
Trigonal pyramidal is the NH3 molecule's molecular shape. The hydrogen atoms are attracted to the lone pair of electrons on the nitrogen atom, which causes the NH3 bond angle to be 107 degrees.
What is Hybridisation?The process of merging two atomic orbitals to produce a new variety of hybridized orbitals is described as hybridization.
Usually, this mixing creates hybrid orbitals with entirely distinct energies, forms, and other characteristics.
Atomic orbitals with the same energy level are principally responsible for hybridization.
However, if the energies of the orbitals are equivalent, the process can involve both fully filled and partially filled orbitals.
We can better understand bond formation, bond energies, and bond lengths by using the hybridization concept, which is an extension of valence bond theory.
Hence, Trigonal pyramidal is the NH3 molecule's molecular shape. The hydrogen atoms are attracted to the lone pair of electrons on the nitrogen atom, which causes the NH3 bond angle to be 107 degrees.
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Rides, r Cost, c5 $25.506Use the table shown to answer problems10-11.10. A state fair charges $8 for generaladmission and $3.50 for each ride. Usethe pattern in the table to find the cost of7 rides and 10 rides. Then write anequation for the pattern.11. Find the cost c for 18 rides.$29.0078$36.0010C= 8 + 3.50rUse the operation symbols in the math palette as needed. Type an equation. Use integers or decimals for anynumbers in the equation.)11. Find the cost c for 18 rides.
We want to know the cost for 7 rides and for 10 rides. We see that for each ride the price increases by $3.50. And thus the price for 7 rides will be:
[tex]29.00+3.50=32.50[/tex]And the price for 10 rides will be:
[tex]36.00+3.50+3.50=39.50+3.50=43.00[/tex]Now, for finding the equation we use that the state fair charges $8 for a general admission, and $3.50 for each ride. This can be written as:
[tex]y=8+3.50x[/tex]where x represents the number of rides.
For example, if we want to know the cost for 18 rides, we replace the value of x by 18, and we get:
[tex]\begin{gathered} y=8+3.50(18) \\ =8+63 \\ =71 \end{gathered}[/tex]Then, the cost for 18 rides is $71.
pleaneu help us were in class and we don't know the answer guys
The slope of the given linear function is found as -3/4.
What is meant by the linear function?A straight line just on coordinate plane is represented by a linear function.The formula for a linear function is f(x) = mx + b, where m and b are real numbers. Isn't it resembling the slope-intercept form of a line, represented by the equation y = mx + b.For the given question, the values for the x and y coordinates are given .
Consider two points;
(x1, y1) = (4, 6)
(x2, y2) = (8, 3)
Slope = m = (y2 - y1)/(x2 - x1)
Put the values.
m = (3 - 6)/(8 - 4)
m = -3/4
Thus, the slope of the given linear function is found as -3/4.
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find linear approxmiation f(x)=x^3+5x^2+4 at a=1
The linear approximation of the function is given by a³ - 3a² +4 + 10ax
The given function is f(x)=x³+5x²+4
Let us find the linear approximation.
L(a) = f(a) + f'(a)(x-a)
let us differentiate the function
f'(x) = 2x²+10x
Let us find the value of the function at the exact point a
f'(a) = 2a²+10a
f(a) = a³+5a²+4
L(a) = f(a) + f'(a)(x-a)
L(a) = a³ + 5a² + 4 + 2a² + 10a (x-a)
L(a) = a³ + 7a² +4 + 10ax - 10a²
L(a) = a³ - 3a² +4 + 10ax
The use of a line to approximate the value of a function at a point is the definition of a linear approximation of either a function. When we see a curve (of a function) and a point on it, we immediately think of the tangent line concept.
If the equation of the tangent line is discovered at the supplied point, one can roughly calculate the value of something similar to the function at every location that is very close to the supplied point using the equation of the tangent line. This concept is also known as the tangent line approximation because the tangent line is utilized. Additionally called linear approximation.
Therefore the linear approximation of the function is given by
a³ - 3a² +4 + 10ax .
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The average daily high temperature in Montreal last week was 12°. This week's average daily high temperature is supposed to be 24° lower. If the high temperature on Friday is equal to this week's average daily high temperature, which of the following could be Friday's high temperature? A. -36° B. -3° C. -12° D. 2°
If the high temperature on Friday is equal to this week's average daily high temperature, the option that could be Friday's high temperature is: C. -12°.
How to find the temperature?Using this formula to find the high temperature
High temperature= Last week average daily high temperature + ( -This week average daily high temperature)
Let plug in the formula
High temperature = 12° + (-24°)
High temperature= -12°
Therefore the correct option is C.
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what is the 1/3 of 24
ANSWER:
8
STEP-BY-STEP EXPLANATION:
They ask us for 1/3 of 24, what we must do multiply both values, just like that
[tex]\frac{1}{3}\cdot24=8[/tex]Which means that 1/3 of 24 is 8
Given: A = B,
CD LAB
Prove: CD bisects ACB
C
A
D
B
As AD = DB, CD bisects ∠ACD
In Δ ACD and ΔBCD
We need to prove that CD bisects ACB
∠A = ∠B
side AC = CB (as angle A and angle B are same)
CD is ⊥ AB
So, ∠ADC = ∠BDC
By SAS Δ ACD and ΔBCD are congurent
In congurent triangles, corresponding angles and sides are equal
So, in Δ ACD and ΔBCD
ACD = DCB
Therefore, as AD = DB, CD bisects ∠ACD
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8. An outlier is going to be added to a data set. Which is most likely to occur? A. an increase in the MAD, but not the IQR B. a decrease in the MAD, but not the IQR C. an increase in the IQR, but not the MAD D. a decrease in the IQR, but not the
Answer;
It causes an increase in the MAD, but not the IQR
Explanation;
Mathematically, we know that an outlier in a dataset represents a value that is at least 2 standard deviations away from the mean value
While MAD represents the mean absolute deviation, IQR represents the interquartile range
It is expected that the outlier affects the value of the standard deviation
By calculating the MAD, we have to subtract values from the mean and square them and this makes the mean absolute deviation affected by the outlier
Hence, we can conclude that the presence of an outlier increases the mean absolute deviation
For the interquartile range, it only moves the lower quartile and the upper quartile same way and thus, it has no effect on it
What are the domain and range of the function represented by the set ofordered pairs?{(-13, 9), (-7,-5), (5, 14), (11,-10)}
Solution:
Given the ordered pairs;
[tex]\lbrace(-13,9),(-7,-5),(5,14),(11,-10)\rbrace[/tex]The domain, x, of the function is;
[tex]x=\lbrace-13,-7,5,11\rbrace[/tex]Then, the range, y, is;
[tex][/tex]The mean mark for the class was 70% there are 30 students in class 20 of whom are boys the mean mark for the mark in test was 62% work out mean for the girls.
The mean mark of the girls is 86.
How is the mean mark calculated?You must first add up all the numbers (3 + 11 + 4 + 6 + 8 + 9 + 6 = 47) before you can determine the mean. The amount is then divided by the number of scores utilized (47 / 7 = 6.7).
Given information:
The number of total students in the class is 30
Given number of boys in the class is 20
Then, the number of girls will be = 30-20
=10
The mean mark of the class = 70×30
= 2100
The guy's average grade is = 62.
Then, mark for the boys = 62×20
= 1240
The mark for the girls = 2100-1240
= 860
Then the mean mark of the girls will be =860/10
= 86
Hence, the mean mark for the girls is 86
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Andrew is home one winter day studying for an exam. It is lunchtime and he is hungry. Instead of making a sandwich from roast beef in the fridge, he drives to taco bell and spends $5 for 2 tacos, a burrito, and a dr. Pepper. He reasons that he can make $10 per hour cutting lawns so he really saves $5 by going to taco bell rather than preparing his own meal. What's wrong with andrews argument?.
Answer:
He cannot save $5 when he is buying something instead of making it himself.
Step-by-step explanation:
He makes $10 from lawn mowing and spends $5 on Taco Bell. He has $5 left.
If he made is lunch, He would have had $10 dollars.
Andrew's argument is flawed because he is not considering all of the costs and benefits associated with his decision to go to Taco Bell instead of preparing his own meal.
What is the argument?An argument is a collection of claims, the premises of which are provided in support of another statement, the conclusion.
There are a few problems with Andrew's argument.
First, he is assuming that the only cost of preparing his own meal is the price of the ingredients. However, there are also opportunity costs associated with preparing his own meal, such as the time he spends making it and the opportunity to do something else during that time (such as study for his exam).
Second, Andrew is assuming that he would have spent the same amount of money on ingredients as he did on his meal at Taco Bell. However, it is possible that the ingredients he would have used to make his own meal would have cost less than $5, in which case he would not have saved as much money as he thinks.
Finally, Andrew is assuming that he would have spent the same amount of time preparing his own meal as he did going to Taco Bell. However, it is possible that it would have taken him longer to prepare his own meal, in which case the opportunity cost of his time would have been even higher.
Overall, Andrew's argument is flawed because he does not evaluate all of the expenses and advantages of his decision to eat at Taco Bell instead of cooking his own dinner.
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